A016187 Expansion of 1/((1-8*x)*(1-11*x)).

1, 19, 273, 3515, 42761, 503139, 5796673, 65860555, 741243321, 8287894259, 92240578673, 1023236299995, 11324318776681, 125117262357379, 1380687932442273, 15222751628953835, 167731742895202841, 1847300971660916499, 20338325086779563473, 223865691142651054075, 2463675524073768441801, 27109654136848307635619

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..950

Index entries for linear recurrences with constant coefficients, signature (19,-88).

Formula

a(n) = (11^(n+1) - 8^(n+1))/3. - Lambert Klasen (lambert.klasen(AT)gmx.net), Feb 05 2005

From Vincenzo Librandi, Feb 09 2011: (Start)

a(n) = 11*a(n-1) + 8^n, a(0)=1.

a(n) = 19*a(n-1) - 88*a(n-2), a(0)=1, a(1)=19. (End)

E.g.f.: (1/3)*(11*exp(11*x) - 8*exp(8*x)). - G. C. Greubel, Nov 14 2024

Mathematica

Table[(11^(n+1)-8^(n+1))/3, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 14 2011 *)
(* Alternative: *)
LinearRecurrence[{19, -88}, {1, 19}, 40] (* G. C. Greubel, Nov 14 2024 *)

Prog

(PARI) for(n=1, 10, print1((11^n-8^n)/3, ", "))
(PARI) MM(n, N) = local(M); M=matrix(n, n); for(i=1, n, for(j=1, n, if(i==j, M[i, j]=N, M[i, j]=1))); M
for(i=1, 10, print1((MM(3, 9)^i)[1, 2], ", "))
(Magma) [(11^(n+1)-8^(n+1))/3: n in [0..40]]; // G. C. Greubel, Nov 14 2024
(SageMath)
A016187=BinaryRecurrenceSequence(19, -88, 1, 19)
print([A016187(n) for n in range(41)]) # G. C. Greubel, Nov 14 2024

Crossrefs

Cf. A016140.

Sequence in context: A016248 A322539 A199819 * A016184 A197742 A322628

Adjacent sequences: A016184 A016185 A016186 * A016188 A016189 A016190

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Extensions

More terms added by G. C. Greubel, Nov 14 2024

Status

approved